Average Error: 0.1 → 0.0
Time: 1.2s
Precision: 64
\[\frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{z}\]
↓
\[4 \cdot \left(\frac{x}{z} - \frac{y}{z}\right) + \left(-2\right)\]
\frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{z}
↓
4 \cdot \left(\frac{x}{z} - \frac{y}{z}\right) + \left(-2\right)
double f(double x, double y, double z) {
        double r950977 = 4.0;
        double r950978 = x;
        double r950979 = y;
        double r950980 = r950978 - r950979;
        double r950981 = z;
        double r950982 = 0.5;
        double r950983 = r950981 * r950982;
        double r950984 = r950980 - r950983;
        double r950985 = r950977 * r950984;
        double r950986 = r950985 / r950981;
        return r950986;
}
↓
double f(double x, double y, double z) {
        double r950987 = 4.0;
        double r950988 = x;
        double r950989 = z;
        double r950990 = r950988 / r950989;
        double r950991 = y;
        double r950992 = r950991 / r950989;
        double r950993 = r950990 - r950992;
        double r950994 = r950987 * r950993;
        double r950995 = 2.0;
        double r950996 = -r950995;
        double r950997 = r950994 + r950996;
        return r950997;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original0.1
Target0.0
Herbie0.0
\[4 \cdot \frac{x}{z} - \left(2 + 4 \cdot \frac{y}{z}\right)\]

Derivation

  1. Initial program 0.1

    \[\frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{z}\]

  2. Taylor expanded around 0 0.0

    \[\leadsto \color{blue}{4 \cdot \frac{x}{z} - \left(4 \cdot \frac{y}{z} + 2\right)}\]

  3. Simplified0.0

    \[\leadsto \color{blue}{4 \cdot \frac{x - y}{z} + \left(-2\right)}\]
  4. Using strategy rm

  5. Applied div-sub0.0

    \[\leadsto 4 \cdot \color{blue}{\left(\frac{x}{z} - \frac{y}{z}\right)} + \left(-2\right)\]

  6. Final simplification0.0

    \[\leadsto 4 \cdot \left(\frac{x}{z} - \frac{y}{z}\right) + \left(-2\right)\]

Reproduce

herbie shell --seed 2019353 
(FPCore (x y z)
  :name "Data.Array.Repa.Algorithms.ColorRamp:rampColorHotToCold from repa-algorithms-3.4.0.1, B"
  :precision binary64

  :herbie-target
  (- (* 4 (/ x z)) (+ 2 (* 4 (/ y z))))

  (/ (* 4 (- (- x y) (* z 0.5))) z))